Problem: $A$ $B$ $C$ If: $ BC = 6x + 5$, $ AB = 4x + 4$, and $ AC = 99$, Find $BC$.
From the diagram, we can see that the total length of ${AC}$ is the sum of ${AB}$ and ${BC}$ $ {AB} + {BC} = {AC}$ Substitute in the expressions that were given for each length: $ {4x + 4} + {6x + 5} = {99}$ Combine like terms: $ 10x + 9 = {99}$ Subtract $9$ from both sides: $ 10x = 90$ Divide both sides by $10$ to find $x$ $ x = 9$ Substitute $9$ for $x$ in the expression that was given for $BC$ $ BC = 6({9}) + 5$ Simplify: $ {BC = 54 + 5}$ Simplify to find ${BC}$ : $ {BC = 59}$